Question

How do you solve the triangle given B = 18°, C = 113°, b = 44?

Answer 1

First, draw a diagram to represent the situation.

Explanation:

Let's start easy, by finding the measure of angle A.

The angles in a triangle add up to 180.

`A = 180 - 113 - 18`

`A = 49˚`

Now, we must find sides a and c. We can do this by Sine's Law:

`(sinA)/a = (sinB)/b = sinC/c`

`(sin49)/a = (sin18)/44 = (sin113)/c`

Start by solving for a (with a scientific calculator)

`a = (sin49 xx 44)/sin18`

`a ~= 107.46`

Next we can solve for c.

`c = (sin113 xx 44)/sin18`

`c ~= 131.07`

So, `A = 49˚, a ~=107.46 and c ~= 131.07`

Practice exercises:

1. Solve the following triangles:

a) `A = 58˚, b = 52 cm and B = 71˚`

b) `A = 122˚, a = 98 ft. and C = 10˚`

Good luck!